LMFDB - Embedded newform 891.2.k.a.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(161,891)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("891.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.3
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71719 - 1.24761i) q^{2} +(0.774180 + 2.38268i) q^{4} +(1.75074 + 2.40969i) q^{5} +(3.03899 - 0.987427i) q^{7} +(0.331430 - 1.02004i) q^{8} -6.32217i q^{10} +(2.38818 + 2.30144i) q^{11} +(1.50453 - 2.07081i) q^{13} +(-6.45046 - 2.09588i) q^{14} +(2.21191 - 1.60705i) q^{16} +(0.807393 - 0.586606i) q^{17} +(-3.66639 - 1.19128i) q^{19} +(-4.38614 + 6.03700i) q^{20} +(-1.22966 - 6.93154i) q^{22} +5.27382i q^{23} +(-1.19643 + 3.68223i) q^{25} +(-5.16715 + 1.67891i) q^{26} +(4.70544 + 6.47649i) q^{28} +(-1.85154 - 5.69844i) q^{29} +(6.43584 + 4.67591i) q^{31} -7.94833 q^{32} -2.11831 q^{34} +(7.69988 + 5.59429i) q^{35} +(1.32852 + 4.08876i) q^{37} +(4.80964 + 6.61990i) q^{38} +(3.03823 - 0.987180i) q^{40} +(-0.411450 + 1.26631i) q^{41} +3.29613i q^{43} +(-3.63471 + 7.47199i) q^{44} +(6.57970 - 9.05618i) q^{46} +(-5.03182 - 1.63494i) q^{47} +(2.59731 - 1.88706i) q^{49} +(6.64851 - 4.83042i) q^{50} +(6.09886 + 1.98164i) q^{52} +(-2.43390 + 3.34997i) q^{53} +(-1.36467 + 9.78400i) q^{55} -3.42715i q^{56} +(-3.93001 + 12.0953i) q^{58} +(11.0565 - 3.59249i) q^{59} +(4.71908 + 6.49525i) q^{61} +(-5.21785 - 16.0589i) q^{62} +(9.22499 + 6.70235i) q^{64} +7.62407 q^{65} -6.61239 q^{67} +(2.02276 + 1.46962i) q^{68} +(-6.24267 - 19.2130i) q^{70} +(-5.64201 - 7.76556i) q^{71} +(-0.706745 + 0.229635i) q^{73} +(2.81987 - 8.67867i) q^{74} -9.65810i q^{76} +(9.53014 + 4.63589i) q^{77} +(6.88586 - 9.47757i) q^{79} +(7.74499 + 2.51650i) q^{80} +(2.28641 - 1.66117i) q^{82} +(2.18571 - 1.58801i) q^{83} +(2.82708 + 0.918574i) q^{85} +(4.11230 - 5.66010i) q^{86} +(3.13907 - 1.67327i) q^{88} +9.15275i q^{89} +(2.52748 - 7.77878i) q^{91} +(-12.5658 + 4.08289i) q^{92} +(6.60084 + 9.08528i) q^{94} +(-3.54829 - 10.9205i) q^{95} +(-7.54954 - 5.48506i) q^{97} -6.81440 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.71719	−	1.24761i	−1.21424	−	0.882197i	−0.218631	−	0.975808i	$-0.570159\pi$
$2$	−1.71719	−	1.24761i	−1.21424	−	0.882197i	−0.995609	+	0.0936108i	$0.970159\pi$
$3$		0			0
$3$		0			0
$4$	0.774180	+	2.38268i	0.387090	+	1.19134i
$5$	1.75074	+	2.40969i	0.782957	+	1.07765i	0.994950	+	0.100376i	$0.0320047\pi$
$5$	1.75074	+	2.40969i	0.782957	+	1.07765i	−0.211993	+	0.977271i	$0.567995\pi$
$6$		0			0
$7$	3.03899	−	0.987427i	1.14863	−	0.373212i	0.328002	−	0.944677i	$-0.393625\pi$
$7$	3.03899	−	0.987427i	1.14863	−	0.373212i	0.820627	+	0.571465i	$0.193625\pi$
$8$	0.331430	−	1.02004i	0.117178	−	0.360638i
$9$		0			0
$10$		−	6.32217i		−	1.99924i
$11$	2.38818	+	2.30144i	0.720062	+	0.693909i
$11$	2.38818	+	2.30144i	0.720062	+	0.693909i
$12$		0			0
$13$	1.50453	−	2.07081i	0.417282	−	0.574340i	−0.547693	−	0.836679i	$-0.684494\pi$
$13$	1.50453	−	2.07081i	0.417282	−	0.574340i	0.964976	+	0.262339i	$0.0844940\pi$
$14$	−6.45046	−	2.09588i	−1.72396	−	0.560148i
$15$		0			0
$16$	2.21191	−	1.60705i	0.552978	−	0.401762i
$17$	0.807393	−	0.586606i	0.195822	−	0.142273i	−0.485554	−	0.874207i	$-0.661382\pi$
$17$	0.807393	−	0.586606i	0.195822	−	0.142273i	0.681376	+	0.731934i	$0.261382\pi$
$18$		0			0
$19$	−3.66639	−	1.19128i	−0.841127	−	0.273299i	−0.143402	−	0.989664i	$-0.545804\pi$
$19$	−3.66639	−	1.19128i	−0.841127	−	0.273299i	−0.697725	+	0.716366i	$0.745804\pi$
$20$	−4.38614	+	6.03700i	−0.980770	+	1.34991i
$21$		0			0
$22$	−1.22966	−	6.93154i	−0.262164	−	1.47781i
$23$			5.27382i			1.09967i	0.835274	+	0.549834i	$0.185309\pi$
$23$			5.27382i			1.09967i	−0.835274	+	0.549834i	$0.814691\pi$
$24$		0			0
$25$	−1.19643	+	3.68223i	−0.239286	+	0.736446i
$26$	−5.16715	+	1.67891i	−1.01336	+	0.329261i
$27$		0			0
$28$	4.70544	+	6.47649i	0.889245	+	1.22394i
$29$	−1.85154	−	5.69844i	−0.343822	−	1.05817i	−0.962212	−	0.272303i	$-0.912215\pi$
$29$	−1.85154	−	5.69844i	−0.343822	−	1.05817i	0.618390	−	0.785871i	$-0.287785\pi$
$30$		0			0
$31$	6.43584	+	4.67591i	1.15591	+	0.839819i	0.989256	−	0.146196i	$-0.0467031\pi$
$31$	6.43584	+	4.67591i	1.15591	+	0.839819i	0.166656	+	0.986015i	$0.446703\pi$
$32$	−7.94833			−1.40508
$33$		0			0
$34$	−2.11831			−0.363287
$35$	7.69988	+	5.59429i	1.30152	+	0.945608i
$36$		0			0
$37$	1.32852	+	4.08876i	0.218407	+	0.672188i	0.998894	+	0.0470160i	$0.0149712\pi$
$37$	1.32852	+	4.08876i	0.218407	+	0.672188i	−0.780487	+	0.625172i	$0.785029\pi$
$38$	4.80964	+	6.61990i	0.780227	+	1.07389i
$39$		0			0
$40$	3.03823	−	0.987180i	0.480386	−	0.156087i
$41$	−0.411450	+	1.26631i	−0.0642576	+	0.197765i	−0.978031	−	0.208460i	$-0.933155\pi$
$41$	−0.411450	+	1.26631i	−0.0642576	+	0.197765i	0.913773	+	0.406225i	$0.133155\pi$
$42$		0			0
$43$			3.29613i			0.502655i	0.967902	+	0.251328i	$0.0808671\pi$
$43$			3.29613i			0.502655i	−0.967902	+	0.251328i	$0.919133\pi$
$44$	−3.63471	+	7.47199i	−0.547953	+	1.12644i
$45$		0			0
$46$	6.57970	−	9.05618i	0.970124	−	1.33526i
$47$	−5.03182	−	1.63494i	−0.733967	−	0.238480i	−0.0818987	−	0.996641i	$-0.526098\pi$
$47$	−5.03182	−	1.63494i	−0.733967	−	0.238480i	−0.652068	+	0.758160i	$0.726098\pi$
$48$		0			0
$49$	2.59731	−	1.88706i	0.371044	−	0.269579i
$50$	6.64851	−	4.83042i	0.940241	−	0.683125i
$51$		0			0
$52$	6.09886	+	1.98164i	0.845760	+	0.274804i
$53$	−2.43390	+	3.34997i	−0.334322	+	0.460154i	−0.942772	−	0.333437i	$-0.891791\pi$
$53$	−2.43390	+	3.34997i	−0.334322	+	0.460154i	0.608450	+	0.793592i	$0.291791\pi$
$54$		0			0
$55$	−1.36467	+	9.78400i	−0.184012	+	1.31927i
$56$		−	3.42715i		−	0.457972i
$57$		0			0
$58$	−3.93001	+	12.0953i	−0.516036	+	1.58820i
$59$	11.0565	−	3.59249i	1.43944	−	0.467702i	0.517716	−	0.855552i	$-0.326782\pi$
$59$	11.0565	−	3.59249i	1.43944	−	0.467702i	0.921722	+	0.387851i	$0.126782\pi$
$60$		0			0
$61$	4.71908	+	6.49525i	0.604216	+	0.831632i	0.996086	−	0.0883887i	$-0.0281717\pi$
$61$	4.71908	+	6.49525i	0.604216	+	0.831632i	−0.391870	+	0.920021i	$0.628172\pi$
$62$	−5.21785	−	16.0589i	−0.662668	−	2.03948i
$63$		0			0
$64$	9.22499	+	6.70235i	1.15312	+	0.837794i
$65$	7.62407			0.945650
$66$		0			0
$67$	−6.61239			−0.807832			−0.403916	−	0.914796i	$-0.632351\pi$
$67$	−6.61239			−0.807832			−0.403916	+	0.914796i	$0.632351\pi$
$68$	2.02276	+	1.46962i	0.245296	+	0.178218i
$69$		0			0
$70$	−6.24267	−	19.2130i	−0.746142	−	2.29639i
$71$	−5.64201	−	7.76556i	−0.669583	−	0.921603i	0.330167	−	0.943922i	$-0.392895\pi$
$71$	−5.64201	−	7.76556i	−0.669583	−	0.921603i	−0.999751	+	0.0223198i	$0.992895\pi$
$72$		0			0
$73$	−0.706745	+	0.229635i	−0.0827183	+	0.0268768i	−0.350084	−	0.936718i	$-0.613847\pi$
$73$	−0.706745	+	0.229635i	−0.0827183	+	0.0268768i	0.267366	+	0.963595i	$0.413847\pi$
$74$	2.81987	−	8.67867i	0.327803	−	1.00888i
$75$		0			0
$76$		−	9.65810i		−	1.10786i
$77$	9.53014	+	4.63589i	1.08606	+	0.528308i
$78$		0			0
$79$	6.88586	−	9.47757i	0.774719	−	1.06631i	−0.221126	−	0.975245i	$-0.570973\pi$
$79$	6.88586	−	9.47757i	0.774719	−	1.06631i	0.995845	−	0.0910643i	$-0.0290269\pi$
$80$	7.74499	+	2.51650i	0.865916	+	0.281353i
$81$		0			0
$82$	2.28641	−	1.66117i	0.252492	−	0.183446i
$83$	2.18571	−	1.58801i	0.239912	−	0.174307i	−0.461332	−	0.887228i	$-0.652628\pi$
$83$	2.18571	−	1.58801i	0.239912	−	0.174307i	0.701244	+	0.712921i	$0.252628\pi$
$84$		0			0
$85$	2.82708	+	0.918574i	0.306640	+	0.0996333i
$86$	4.11230	−	5.66010i	0.443441	−	0.610344i
$87$		0			0
$88$	3.13907	−	1.67327i	0.334626	−	0.178371i
$89$			9.15275i			0.970189i	0.874462	+	0.485095i	$0.161215\pi$
$89$			9.15275i			0.970189i	−0.874462	+	0.485095i	$0.838785\pi$
$90$		0			0
$91$	2.52748	−	7.77878i	0.264952	−	0.815438i
$92$	−12.5658	+	4.08289i	−1.31008	+	0.425671i
$93$		0			0
$94$	6.60084	+	9.08528i	0.680825	+	0.937075i
$95$	−3.54829	−	10.9205i	−0.364046	−	1.12042i
$96$		0			0
$97$	−7.54954	−	5.48506i	−0.766540	−	0.556924i	0.134370	−	0.990931i	$-0.457099\pi$
$97$	−7.54954	−	5.48506i	−0.766540	−	0.556924i	−0.900909	+	0.434008i	$0.857099\pi$
$98$	−6.81440			−0.688359
$99$		0			0
$100$	−9.69983			−0.969983
$101$	6.03378	+	4.38379i	0.600383	+	0.436204i	0.846015	−	0.533159i	$-0.178995\pi$
$101$	6.03378	+	4.38379i	0.600383	+	0.436204i	−0.245632	+	0.969363i	$0.578995\pi$
$102$		0			0
$103$	−4.63094	−	14.2526i	−0.456300	−	1.40435i	−0.869602	−	0.493753i	$-0.835625\pi$
$103$	−4.63094	−	14.2526i	−0.456300	−	1.40435i	0.413302	−	0.910594i	$-0.364375\pi$
$104$	−1.61366	−	2.22101i	−0.158232	−	0.217788i
$105$		0			0
$106$	8.35896	−	2.71599i	0.811894	−	0.263800i
$107$	5.29261	−	16.2890i	0.511656	−	1.57472i	−0.277628	−	0.960689i	$-0.589548\pi$
$107$	5.29261	−	16.2890i	0.511656	−	1.57472i	0.789285	−	0.614028i	$-0.210452\pi$
$108$		0			0
$109$		−	0.449919i		−	0.0430944i	−0.999768	−	0.0215472i	$-0.993141\pi$
$109$		−	0.449919i		−	0.0430944i	0.999768	−	0.0215472i	$-0.00685922\pi$
$110$	14.5501	−	15.0985i	1.38729	−	1.43958i
$111$		0			0
$112$	5.13513	−	7.06790i	0.485224	−	0.667854i
$113$	3.96010	+	1.28672i	0.372535	+	0.121044i	0.489300	−	0.872116i	$-0.337252\pi$
$113$	3.96010	+	1.28672i	0.372535	+	0.121044i	−0.116765	+	0.993160i	$0.537252\pi$
$114$		0			0
$115$	−12.7083	+	9.23312i	−1.18505	+	0.860993i
$116$	12.1441	−	8.82324i	1.12756	−	0.819217i
$117$		0			0
$118$	−23.4683	−	7.62530i	−2.16043	−	0.701966i
$119$	1.87443	−	2.57993i	0.171829	−	0.236502i
$120$		0			0
$121$	0.406780	+	10.9925i	0.0369800	+	0.999316i
$122$		−	17.0412i		−	1.54284i
$123$		0			0
$124$	−6.15871	+	18.9546i	−0.553068	+	1.70217i
$125$	3.19613	−	1.03849i	0.285871	−	0.0928850i
$126$		0			0
$127$	9.90407	+	13.6318i	0.878844	+	1.20962i	0.976740	+	0.214428i	$0.0687888\pi$
$127$	9.90407	+	13.6318i	0.878844	+	1.20962i	−0.0978959	+	0.995197i	$0.531211\pi$
$128$	−2.56682	−	7.89986i	−0.226877	−	0.698256i
$129$		0			0
$130$	−13.0920	−	9.51190i	−1.14825	−	0.834249i
$131$	−14.3217			−1.25129			−0.625647	−	0.780106i	$-0.715165\pi$
$131$	−14.3217			−1.25129			−0.625647	+	0.780106i	$0.715165\pi$
$132$		0			0
$133$	−12.3184			−1.06814
$134$	11.3548	+	8.24971i	0.980901	+	0.712667i
$135$		0			0
$136$	−0.330765	−	1.01799i	−0.0283629	−	0.0872920i
$137$	−1.41576	−	1.94863i	−0.120956	−	0.166482i	0.744245	−	0.667907i	$-0.232810\pi$
$137$	−1.41576	−	1.94863i	−0.120956	−	0.166482i	−0.865201	+	0.501424i	$0.832810\pi$
$138$		0			0
$139$	4.05604	−	1.31789i	0.344029	−	0.111782i	−0.131906	−	0.991262i	$-0.542110\pi$
$139$	4.05604	−	1.31789i	0.344029	−	0.111782i	0.475935	+	0.879480i	$0.342110\pi$
$140$	−7.36832	+	22.6774i	−0.622737	+	1.91659i
$141$		0			0
$142$			20.3740i			1.70975i
$143$	8.35893	−	1.48288i	0.699009	−	0.124004i
$144$		0			0
$145$	10.4899	−	14.4381i	0.871141	−	1.19902i
$146$	1.50012	+	0.487417i	0.124150	+	0.0403389i
$147$		0			0
$148$	−8.71370	+	6.33087i	−0.716261	+	0.520394i
$149$	3.21329	−	2.33459i	0.263243	−	0.191257i	−0.448333	−	0.893867i	$-0.647982\pi$
$149$	3.21329	−	2.33459i	0.263243	−	0.191257i	0.711575	+	0.702610i	$0.247982\pi$
$150$		0			0
$151$	16.4430	+	5.34267i	1.33812	+	0.434780i	0.888678	−	0.458531i	$-0.151624\pi$
$151$	16.4430	+	5.34267i	1.33812	+	0.434780i	0.449438	+	0.893312i	$0.351624\pi$
$152$	−2.43031	+	3.34503i	−0.197124	+	0.271318i
$153$		0			0
$154$	−10.5813	−	19.8507i	−0.852665	−	1.59961i
$155$			23.6947i			1.90321i
$156$		0			0
$157$	0.112621	−	0.346613i	0.00898815	−	0.0276627i	−0.946462	−	0.322816i	$-0.895371\pi$
$157$	0.112621	−	0.346613i	0.00898815	−	0.0276627i	0.955450	+	0.295153i	$0.0953706\pi$
$158$	−23.6487	+	7.68393i	−1.88139	+	0.611301i
$159$		0			0
$160$	−13.9155	−	19.1530i	−1.10012	−	1.51418i
$161$	5.20751	+	16.0271i	0.410410	+	1.26311i
$162$		0			0
$163$	−2.44510	−	1.77647i	−0.191515	−	0.139144i	0.487896	−	0.872902i	$-0.337765\pi$
$163$	−2.44510	−	1.77647i	−0.191515	−	0.139144i	−0.679411	+	0.733758i	$0.737765\pi$
$164$	−3.33575			−0.260479
$165$		0			0
$166$	−5.73450			−0.445084
$167$	6.22872	+	4.52543i	0.481992	+	0.350188i	0.802097	−	0.597194i	$-0.203718\pi$
$167$	6.22872	+	4.52543i	0.481992	+	0.350188i	−0.320104	+	0.947382i	$0.603718\pi$
$168$		0			0
$169$	1.99258	+	6.13253i	0.153275	+	0.471733i
$170$	−3.70862	−	5.10447i	−0.284438	−	0.391495i
$171$		0			0
$172$	−7.85363	+	2.55180i	−0.598833	+	0.194573i
$173$	−3.43195	+	10.5625i	−0.260926	+	0.803049i	0.731678	+	0.681651i	$0.238738\pi$
$173$	−3.43195	+	10.5625i	−0.260926	+	0.803049i	−0.992604	+	0.121398i	$0.961262\pi$
$174$		0			0
$175$			12.3716i			0.935208i
$176$	8.98096	+	1.25266i	0.676966	+	0.0944228i
$177$		0			0
$178$	11.4191	−	15.7170i	0.855898	−	1.17804i
$179$	−7.87767	−	2.55961i	−0.588805	−	0.191314i	−0.000563753	−	1.00000i	$-0.500179\pi$
$179$	−7.87767	−	2.55961i	−0.588805	−	0.191314i	−0.588241	+	0.808686i	$0.700179\pi$
$180$		0			0
$181$	−13.8429	+	10.0575i	−1.02894	+	0.747565i	−0.968095	−	0.250582i	$-0.919378\pi$
$181$	−13.8429	+	10.0575i	−1.02894	+	0.747565i	−0.0608402	+	0.998148i	$0.519378\pi$
$182$	−14.0451	+	10.2044i	−1.04109	+	0.756398i
$183$		0			0
$184$	5.37950	+	1.74791i	0.396582	+	0.128857i
$185$	−7.52676	+	10.3597i	−0.553378	+	0.761660i
$186$		0			0
$187$	3.27823	+	0.457246i	0.239728	+	0.0334372i
$188$		−	13.2550i		−	0.966718i
$189$		0			0
$190$	−7.53148	+	23.1795i	−0.546391	+	1.68162i
$191$	−10.3620	+	3.36683i	−0.749771	+	0.243615i	−0.658883	−	0.752246i	$-0.728971\pi$
$191$	−10.3620	+	3.36683i	−0.749771	+	0.243615i	−0.0908882	+	0.995861i	$0.528971\pi$
$192$		0			0
$193$	6.36278	+	8.75762i	0.458003	+	0.630387i	0.974093	−	0.226147i	$-0.0726130\pi$
$193$	6.36278	+	8.75762i	0.458003	+	0.630387i	−0.516090	+	0.856534i	$0.672613\pi$
$194$	6.12078	+	18.8378i	0.439447	+	1.35248i
$195$		0			0
$196$	6.50704	+	4.72764i	0.464788	+	0.337688i
$197$	−1.78800			−0.127390			−0.0636948	−	0.997969i	$-0.520288\pi$
$197$	−1.78800			−0.127390			−0.0636948	+	0.997969i	$0.520288\pi$
$198$		0			0
$199$	0.534305			0.0378759			0.0189379	−	0.999821i	$-0.493972\pi$
$199$	0.534305			0.0378759			0.0189379	+	0.999821i	$0.493972\pi$
$200$	3.35948	+	2.44081i	0.237551	+	0.172591i
$201$		0			0
$202$	−4.89188	−	15.0557i	−0.344191	−	1.05931i
$203$	−11.2536	−	15.4892i	−0.789847	−	1.08713i
$204$		0			0
$205$	−3.77177	+	1.22552i	−0.263432	+	0.0855941i
$206$	−9.82949	+	30.2521i	−0.684853	+	2.10776i
$207$		0			0
$208$		−	6.99831i		−	0.485246i
$209$	−6.01433	−	11.2830i	−0.416020	−	0.780458i
$210$		0			0
$211$	−3.02539	+	4.16409i	−0.208276	+	0.286668i	−0.900357	−	0.435153i	$-0.856694\pi$
$211$	−3.02539	+	4.16409i	−0.208276	+	0.286668i	0.692080	+	0.721820i	$0.256694\pi$
$212$	−9.86620	−	3.20572i	−0.677613	−	0.220170i
$213$		0			0
$214$	−29.4108	+	21.3682i	−2.01048	+	1.46070i
$215$	−7.94266	+	5.77068i	−0.541685	+	0.393557i
$216$		0			0
$217$	24.1756	+	7.85512i	1.64114	+	0.533240i
$218$	−0.561325	+	0.772598i	−0.0380178	+	0.0523270i
$219$		0			0
$220$	−24.3686	+	4.32301i	−1.64293	+	0.291457i
$221$		−	2.55453i		−	0.171836i
$222$		0			0
$223$	1.29767	−	3.99381i	0.0868983	−	0.267445i	−0.898159	−	0.439670i	$-0.855095\pi$
$223$	1.29767	−	3.99381i	0.0868983	−	0.267445i	0.985058	+	0.172224i	$0.0550954\pi$
$224$	−24.1549	+	7.84839i	−1.61391	+	0.524393i
$225$		0			0
$226$	−5.19494	−	7.15023i	−0.345562	−	0.475626i
$227$	−5.16611	−	15.8996i	−0.342887	−	1.05530i	−0.962705	−	0.270552i	$-0.912794\pi$
$227$	−5.16611	−	15.8996i	−0.342887	−	1.05530i	0.619819	−	0.784745i	$-0.287206\pi$
$228$		0			0
$229$	21.0325	+	15.2810i	1.38986	+	1.00980i	0.995880	+	0.0906785i	$0.0289036\pi$
$229$	21.0325	+	15.2810i	1.38986	+	1.00980i	0.393984	+	0.919117i	$0.371096\pi$
$230$	33.3420			2.19851
$231$		0			0
$232$	−6.42628			−0.421906
$233$	−14.0790	−	10.2290i	−0.922345	−	0.670123i	0.0217619	−	0.999763i	$-0.493072\pi$
$233$	−14.0790	−	10.2290i	−0.922345	−	0.670123i	−0.944107	+	0.329641i	$0.893072\pi$
$234$		0			0
$235$	−4.86974	−	14.9875i	−0.317667	−	0.977677i
$236$	17.1195	+	23.5630i	1.11438	+	1.53382i
$237$		0			0
$238$	−6.43751	+	2.09167i	−0.417282	+	0.135583i
$239$	−0.770057	+	2.36999i	−0.0498109	+	0.153302i	−0.972868	−	0.231361i	$-0.925682\pi$
$239$	−0.770057	+	2.36999i	−0.0498109	+	0.153302i	0.923057	+	0.384663i	$0.125682\pi$
$240$		0			0
$241$		−	22.8683i		−	1.47308i	−0.676394	−	0.736540i	$-0.736458\pi$
$241$		−	22.8683i		−	1.47308i	0.676394	−	0.736540i	$-0.263542\pi$
$242$	13.0159	−	19.3837i	0.836691	−	1.24603i
$243$		0			0
$244$	−11.8227	+	16.2725i	−0.756871	+	1.04174i
$245$	9.09445	+	2.95497i	0.581023	+	0.188786i
$246$		0			0
$247$	−7.98312	+	5.80008i	−0.507954	+	0.369050i
$248$	6.90264	−	5.01506i	0.438318	−	0.318457i
$249$		0			0
$250$	−6.78401	−	2.20426i	−0.429059	−	0.139410i
$251$	5.77288	−	7.94569i	0.364381	−	0.501528i	−0.586982	−	0.809600i	$-0.699684\pi$
$251$	5.77288	−	7.94569i	0.364381	−	0.501528i	0.951363	+	0.308073i	$0.0996840\pi$
$252$		0			0
$253$	−12.1374	+	12.5948i	−0.763070	+	0.791830i
$254$		−	35.7649i		−	2.24409i
$255$		0			0
$256$	1.59902	−	4.92126i	0.0999385	−	0.307579i
$257$	−14.1588	+	4.60048i	−0.883203	+	0.286970i	−0.715287	−	0.698831i	$-0.753704\pi$
$257$	−14.1588	+	4.60048i	−0.883203	+	0.286970i	−0.167917	+	0.985801i	$0.553704\pi$
$258$		0			0
$259$	8.07470	+	11.1139i	0.501737	+	0.690582i
$260$	5.90240	+	18.1657i	0.366051	+	1.12659i
$261$		0			0
$262$	24.5932	+	17.8680i	1.51937	+	1.10389i
$263$	5.92380			0.365277			0.182639	−	0.983180i	$-0.441536\pi$
$263$	5.92380			0.365277			0.182639	+	0.983180i	$0.441536\pi$
$264$		0			0
$265$	−12.3335			−0.757644
$266$	21.1531	+	15.3686i	1.29698	+	0.942311i
$267$		0			0
$268$	−5.11918	−	15.7552i	−0.312704	−	0.962403i
$269$	−3.97084	−	5.46539i	−0.242106	−	0.333230i	0.670621	−	0.741800i	$-0.266028\pi$
$269$	−3.97084	−	5.46539i	−0.242106	−	0.333230i	−0.912727	+	0.408570i	$0.866028\pi$
$270$		0			0
$271$	−6.02268	+	1.95689i	−0.365852	+	0.118872i	−0.486173	−	0.873863i	$-0.661608\pi$
$271$	−6.02268	+	1.95689i	−0.365852	+	0.118872i	0.120321	+	0.992735i	$0.461608\pi$
$272$	0.843180	−	2.59504i	0.0511253	−	0.157348i
$273$		0			0
$274$			5.11249i			0.308857i
$275$	−11.3317	+	6.04031i	−0.683328	+	0.364245i
$276$		0			0
$277$	−1.22289	+	1.68317i	−0.0734766	+	0.101132i	−0.844173	−	0.536070i	$-0.819908\pi$
$277$	−1.22289	+	1.68317i	−0.0734766	+	0.101132i	0.770697	+	0.637202i	$0.219908\pi$
$278$	−8.60922	−	2.79731i	−0.516347	−	0.167771i
$279$		0			0
$280$	8.25837	−	6.00006i	0.493532	−	0.358572i
$281$	−5.82179	+	4.22978i	−0.347299	+	0.252327i	−0.747735	−	0.663997i	$-0.768859\pi$
$281$	−5.82179	+	4.22978i	−0.347299	+	0.252327i	0.400436	+	0.916325i	$0.368859\pi$
$282$		0			0
$283$	−22.8994	−	7.44045i	−1.36123	−	0.442289i	−0.464773	−	0.885430i	$-0.653864\pi$
$283$	−22.8994	−	7.44045i	−1.36123	−	0.442289i	−0.896452	+	0.443141i	$0.853864\pi$
$284$	14.1349	−	19.4551i	0.838753	−	1.15444i
$285$		0			0
$286$	−16.2040	−	7.88233i	−0.958161	−	0.466092i
$287$			4.25458i			0.251140i
$288$		0			0
$289$	−4.94551	+	15.2207i	−0.290912	+	0.895336i
$290$	−36.0265	+	11.7057i	−2.11555	+	0.687383i
$291$		0			0
$292$	−1.09430	−	1.50617i	−0.0640388	−	0.0881419i
$293$	−6.72926	−	20.7105i	−0.393128	−	1.20992i	−0.930410	−	0.366520i	$-0.880549\pi$
$293$	−6.72926	−	20.7105i	−0.393128	−	1.20992i	0.537282	−	0.843402i	$-0.319451\pi$
$294$		0			0
$295$	28.0140	+	20.3533i	1.63104	+	1.18502i
$296$	4.61100			0.268009
$297$		0			0
$298$	−8.43051			−0.488366
$299$	10.9211	+	7.93464i	0.631583	+	0.458872i
$300$		0			0
$301$	3.25469	+	10.0169i	0.187597	+	0.577364i
$302$	−21.5703	−	29.6890i	−1.24123	−	1.70841i
$303$		0			0
$304$	−10.0242	+	3.25706i	−0.574926	+	0.186805i
$305$	−7.38967	+	22.7431i	−0.423131	+	1.30226i
$306$		0			0
$307$		−	27.7403i		−	1.58322i	−0.611023	−	0.791612i	$-0.709242\pi$
$307$		−	27.7403i		−	1.58322i	0.611023	−	0.791612i	$-0.290758\pi$
$308$	−3.66779	+	26.2963i	−0.208992	+	1.49837i
$309$		0			0
$310$	29.5619	−	40.6885i	1.67900	−	2.31095i
$311$	20.6834	+	6.72045i	1.17285	+	0.381082i	0.829706	−	0.558201i	$-0.188508\pi$
$311$	20.6834	+	6.72045i	1.17285	+	0.381082i	0.343144	+	0.939283i	$0.388508\pi$
$312$		0			0
$313$	−4.51010	+	3.27678i	−0.254926	+	0.185215i	−0.707907	−	0.706306i	$-0.750360\pi$
$313$	−4.51010	+	3.27678i	−0.254926	+	0.185215i	0.452981	+	0.891520i	$0.350360\pi$
$314$	−0.625831	+	0.454693i	−0.0353177	+	0.0256598i
$315$		0			0
$316$	27.9129	+	9.06945i	1.57022	+	0.510197i
$317$	8.02289	−	11.0426i	0.450610	−	0.620212i	−0.521918	−	0.852996i	$-0.674783\pi$
$317$	8.02289	−	11.0426i	0.450610	−	0.620212i	0.972529	+	0.232784i	$0.0747834\pi$
$318$		0			0
$319$	8.69281	−	17.8701i	0.486704	−	1.00053i
$320$			33.9635i			1.89862i
$321$		0			0
$322$	11.0533	−	34.0186i	0.615977	−	1.89578i
$323$	−3.65903	+	1.18889i	−0.203594	+	0.0661517i
$324$		0			0
$325$	5.82514	+	8.01761i	0.323121	+	0.444737i
$326$	1.98236	+	6.10108i	0.109793	+	0.337908i
$327$		0			0
$328$	1.15532	+	0.839389i	0.0637918	+	0.0463475i
$329$	−16.9060			−0.932059
$330$		0			0
$331$	7.95544			0.437270			0.218635	−	0.975807i	$-0.429840\pi$
$331$	7.95544			0.437270			0.218635	+	0.975807i	$0.429840\pi$
$332$	5.47585	+	3.97843i	0.300526	+	0.218345i
$333$		0			0
$334$	−5.04993	−	15.5421i	−0.276320	−	0.850424i
$335$	−11.5766	−	15.9338i	−0.632497	−	0.870558i
$336$		0			0
$337$	−29.8353	+	9.69408i	−1.62523	+	0.528070i	−0.973169	−	0.230093i	$-0.926097\pi$
$337$	−29.8353	+	9.69408i	−1.62523	+	0.528070i	−0.652065	+	0.758163i	$0.726097\pi$
$338$	4.22939	−	13.0167i	0.230048	−	0.708016i
$339$		0			0
$340$			7.44717i			0.403879i
$341$	4.60861	+	25.9786i	0.249570	+	1.40682i
$342$		0			0
$343$	−7.11752	+	9.79643i	−0.384310	+	0.528957i
$344$	3.36218	+	1.09244i	0.181277	+	0.0589003i
$345$		0			0
$346$	19.0712	−	13.8560i	1.02527	−	0.744905i
$347$	1.83775	−	1.33520i	0.0986553	−	0.0716773i	−0.537364	−	0.843350i	$-0.680580\pi$
$347$	1.83775	−	1.33520i	0.0986553	−	0.0716773i	0.636019	+	0.771673i	$0.280580\pi$
$348$		0			0
$349$	−26.0063	−	8.44995i	−1.39208	−	0.452316i	−0.485461	−	0.874258i	$-0.661348\pi$
$349$	−26.0063	−	8.44995i	−1.39208	−	0.452316i	−0.906623	+	0.421943i	$0.861348\pi$
$350$	15.4350	−	21.2445i	0.825037	−	1.13557i
$351$		0			0
$352$	−18.9820	−	18.2926i	−1.01174	−	0.974997i
$353$		−	19.9733i		−	1.06307i	−0.847036	−	0.531535i	$-0.821615\pi$
$353$		−	19.9733i		−	1.06307i	0.847036	−	0.531535i	$-0.178385\pi$
$354$		0			0
$355$	8.83490	−	27.1910i	0.468908	−	1.44315i
$356$	−21.8081	+	7.08587i	−1.15583	+	0.375551i
$357$		0			0
$358$	10.3341	+	14.2237i	0.546174	+	0.751743i
$359$	−6.60849	−	20.3388i	−0.348783	−	1.07344i	−0.959527	−	0.281615i	$-0.909130\pi$
$359$	−6.60849	−	20.3388i	−0.348783	−	1.07344i	0.610745	−	0.791827i	$-0.290870\pi$
$360$		0			0
$361$	−3.34807	−	2.43251i	−0.176214	−	0.128027i
$362$	36.3188			1.90887
$363$		0			0
$364$	20.4911			1.07402
$365$	−1.79068	−	1.30101i	−0.0937285	−	0.0680978i
$366$		0			0
$367$	−5.94919	−	18.3097i	−0.310545	−	0.955759i	−0.977550	−	0.210706i	$-0.932424\pi$
$367$	−5.94919	−	18.3097i	−0.310545	−	0.955759i	0.667005	−	0.745054i	$-0.267576\pi$
$368$	8.47529	+	11.6652i	0.441805	+	0.608093i
$369$		0			0
$370$	25.8498	−	8.39911i	1.34387	−	0.436649i
$371$	−4.08873	+	12.5838i	−0.212276	+	0.653320i
$372$		0			0
$373$		−	6.89609i		−	0.357066i	−0.983934	−	0.178533i	$-0.942865\pi$
$373$		−	6.89609i		−	0.357066i	0.983934	−	0.178533i	$-0.0571351\pi$
$374$	−5.05890	−	4.87515i	−0.261589	−	0.252088i
$375$		0			0
$376$	−3.33540	+	4.59078i	−0.172010	+	0.236752i
$377$	−14.5861	−	4.73931i	−0.751222	−	0.244087i
$378$		0			0
$379$	27.7790	−	20.1826i	1.42691	−	1.03671i	0.436329	−	0.899787i	$-0.356278\pi$
$379$	27.7790	−	20.1826i	1.42691	−	1.03671i	0.990582	−	0.136924i	$-0.0437215\pi$
$380$	23.2731	−	16.9089i	1.19388	−	0.867407i
$381$		0			0
$382$	21.9941	+	7.14633i	1.12532	+	0.365638i
$383$	−0.940164	+	1.29403i	−0.0480402	+	0.0661216i	−0.832361	−	0.554233i	$-0.813011\pi$
$383$	−0.940164	+	1.29403i	−0.0480402	+	0.0661216i	0.784321	+	0.620355i	$0.213011\pi$
$384$		0			0
$385$	5.51378	+	31.0810i	0.281008	+	1.58403i
$386$		−	22.9768i		−	1.16949i
$387$		0			0
$388$	7.22445	−	22.2346i	0.366766	−	1.12879i
$389$	22.5779	−	7.33601i	1.14475	−	0.371951i	0.325584	−	0.945513i	$-0.394439\pi$
$389$	22.5779	−	7.33601i	1.14475	−	0.371951i	0.819162	+	0.573562i	$0.194439\pi$
$390$		0			0
$391$	3.09365	+	4.25805i	0.156453	+	0.215339i
$392$	−1.06404	−	3.27478i	−0.0537422	−	0.165401i
$393$		0			0
$394$	3.07034	+	2.23073i	0.154682	+	0.112383i
$395$	34.8934			1.75568
$396$		0			0
$397$	−15.1190			−0.758803			−0.379401	−	0.925232i	$-0.623870\pi$
$397$	−15.1190			−0.758803			−0.379401	+	0.925232i	$0.623870\pi$
$398$	−0.917506	−	0.666607i	−0.0459904	−	0.0334140i
$399$		0			0
$400$	3.27113	+	10.0675i	0.163556	+	0.503375i
$401$	15.3082	+	21.0699i	0.764454	+	1.05218i	0.996831	+	0.0795544i	$0.0253497\pi$
$401$	15.3082	+	21.0699i	0.764454	+	1.05218i	−0.232377	+	0.972626i	$0.574650\pi$
$402$		0			0
$403$	19.3659	−	6.29235i	0.964683	−	0.313444i
$404$	−5.77396	+	17.7704i	−0.287265	+	0.884111i
$405$		0			0
$406$			40.6382i			2.01684i
$407$	−6.23728	+	12.8222i	−0.309171	+	0.635572i
$408$		0			0
$409$	−5.04394	+	6.94239i	−0.249407	+	0.343279i	−0.915303	−	0.402765i	$-0.868049\pi$
$409$	−5.04394	+	6.94239i	−0.249407	+	0.343279i	0.665897	+	0.746044i	$0.268049\pi$
$410$	8.00583	+	2.60125i	0.395380	+	0.128467i
$411$		0			0
$412$	30.3741	−	22.0681i	1.49643	−	1.08722i
$413$	30.0533	−	21.8350i	1.47883	−	1.07443i
$414$		0			0
$415$	7.65322	+	2.48668i	0.375682	+	0.122066i
$416$	−11.9585	+	16.4595i	−0.586314	+	0.806993i
$417$		0			0
$418$	−3.74901	+	26.8786i	−0.183370	+	1.31467i
$419$		−	17.8881i		−	0.873892i	−0.899488	−	0.436946i	$-0.856060\pi$
$419$		−	17.8881i		−	0.873892i	0.899488	−	0.436946i	$-0.143940\pi$
$420$		0			0
$421$	−1.07540	+	3.30975i	−0.0524120	+	0.161307i	−0.973836	−	0.227250i	$-0.927027\pi$
$421$	−1.07540	+	3.30975i	−0.0524120	+	0.161307i	0.921424	+	0.388558i	$0.127027\pi$
$422$	10.3904	−	3.37603i	0.505795	−	0.164343i
$423$		0			0
$424$	2.61043	+	3.59295i	0.126774	+	0.174489i
$425$	1.19403	+	3.67484i	0.0579189	+	0.178256i
$426$		0			0
$427$	20.7548	+	15.0792i	1.00440	+	0.729736i
$428$	42.9089			2.07408
$429$		0			0
$430$	20.8387			1.00493
$431$	−22.8883	−	16.6293i	−1.10249	−	0.801005i	−0.121025	−	0.992650i	$-0.538618\pi$
$431$	−22.8883	−	16.6293i	−1.10249	−	0.801005i	−0.981464	+	0.191644i	$0.938618\pi$
$432$		0			0
$433$	1.03161	+	3.17496i	0.0495758	+	0.152579i	0.972780	−	0.231732i	$-0.0744392\pi$
$433$	1.03161	+	3.17496i	0.0495758	+	0.152579i	−0.923204	+	0.384311i	$0.874439\pi$
$434$	−31.7140	−	43.6506i	−1.52232	−	2.09529i
$435$		0			0
$436$	1.07201	−	0.348318i	0.0513401	−	0.0166814i
$437$	6.28261	−	19.3359i	0.300538	−	0.924961i
$438$		0			0
$439$		−	15.1602i		−	0.723556i	−0.932264	−	0.361778i	$-0.882170\pi$
$439$		−	15.1602i		−	0.723556i	0.932264	−	0.361778i	$-0.117830\pi$
$440$	9.52776	+	4.63473i	0.454218	+	0.220952i
$441$		0			0
$442$	−3.18706	+	4.38662i	−0.151593	+	0.208650i
$443$	−10.0392	−	3.26193i	−0.476976	−	0.154979i	0.0606557	−	0.998159i	$-0.480681\pi$
$443$	−10.0392	−	3.26193i	−0.476976	−	0.154979i	−0.537632	+	0.843180i	$0.680681\pi$
$444$		0			0
$445$	−22.0553	+	16.0241i	−1.04552	+	0.759616i
$446$	−7.21109	+	5.23916i	−0.341455	+	0.248081i
$447$		0			0
$448$	34.6527	+	11.2593i	1.63719	+	0.531954i
$449$	−9.24496	+	12.7246i	−0.436297	+	0.600511i	−0.969384	−	0.245549i	$-0.921032\pi$
$449$	−9.24496	+	12.7246i	−0.436297	+	0.600511i	0.533087	+	0.846060i	$0.321032\pi$
$450$		0			0
$451$	−3.89695	+	2.07725i	−0.183500	+	0.0978140i
$452$			10.4318i			0.490671i
$453$		0			0
$454$	−10.9654	+	33.7481i	−0.514633	+	1.58388i
$455$	23.1694	−	7.52821i	1.08620	−	0.352928i
$456$		0			0
$457$	−1.79378	−	2.46893i	−0.0839097	−	0.115492i	0.764999	−	0.644032i	$-0.222740\pi$
$457$	−1.79378	−	2.46893i	−0.0839097	−	0.115492i	−0.848908	+	0.528540i	$0.822740\pi$
$458$	−17.0521	−	52.4808i	−0.796790	−	2.45227i
$459$		0			0
$460$	−31.8381	−	23.1317i	−1.48446	−	1.07852i
$461$	−0.491689			−0.0229002			−0.0114501	−	0.999934i	$-0.503645\pi$
$461$	−0.491689			−0.0229002			−0.0114501	+	0.999934i	$0.503645\pi$
$462$		0			0
$463$	8.98358			0.417502			0.208751	−	0.977969i	$-0.433060\pi$
$463$	8.98358			0.417502			0.208751	+	0.977969i	$0.433060\pi$
$464$	−13.2531	−	9.62895i	−0.615260	−	0.447013i
$465$		0			0
$466$	11.4145	+	35.1303i	0.528767	+	1.62738i
$467$	−1.33494	−	1.83738i	−0.0617735	−	0.0850239i	0.777013	−	0.629485i	$-0.216734\pi$
$467$	−1.33494	−	1.83738i	−0.0617735	−	0.0850239i	−0.838786	+	0.544461i	$0.816734\pi$
$468$		0			0
$469$	−20.0950	+	6.52925i	−0.927899	+	0.301493i
$470$	−10.3364	+	31.8120i	−0.476780	+	1.46738i
$471$		0			0
$472$		−	12.4687i		−	0.573921i
$473$	−7.58583	+	7.87174i	−0.348797	+	0.361943i
$474$		0			0
$475$	8.77315	−	12.0752i	0.402540	−	0.554048i
$476$	7.59829	+	2.46883i	0.348267	+	0.113159i
$477$		0			0
$478$	4.27918	−	3.10900i	0.195725	−	0.142202i
$479$	−9.37003	+	6.80772i	−0.428127	+	0.311053i	−0.780900	−	0.624656i	$-0.785239\pi$
$479$	−9.37003	+	6.80772i	−0.428127	+	0.311053i	0.352772	+	0.935709i	$0.385239\pi$
$480$		0			0
$481$	10.4658	+	3.40056i	0.477202	+	0.155052i
$482$	−28.5309	+	39.2694i	−1.29955	+	1.78867i
$483$		0			0
$484$	−25.8766	+	9.47938i	−1.17621	+	0.430881i
$485$		−	27.7950i		−	1.26211i
$486$		0			0
$487$	11.3865	−	35.0439i	0.515970	−	1.58799i	−0.265541	−	0.964100i	$-0.585551\pi$
$487$	11.3865	−	35.0439i	0.515970	−	1.58799i	0.781511	−	0.623892i	$-0.214449\pi$
$488$	8.18945	−	2.66091i	0.370719	−	0.120454i
$489$		0			0
$490$	−11.9303	−	16.4206i	−0.538955	−	0.741808i
$491$	4.30496	+	13.2493i	0.194280	+	0.597933i	0.999984	+	0.00561479i	$0.00178725\pi$
$491$	4.30496	+	13.2493i	0.194280	+	0.597933i	−0.805704	+	0.592318i	$0.798213\pi$
$492$		0			0
$493$	−4.83766	−	3.51476i	−0.217877	−	0.158297i
$494$	20.9448			0.942353
$495$		0			0
$496$	21.7500			0.976602
$497$	−24.8139	−	18.0284i	−1.11306	−	0.808683i
$498$		0			0
$499$	3.90314	+	12.0126i	0.174729	+	0.537760i	0.999621	−	0.0275302i	$-0.00876425\pi$
$499$	3.90314	+	12.0126i	0.174729	+	0.537760i	−0.824892	+	0.565290i	$0.808764\pi$
$500$	4.94876	+	6.81139i	0.221315	+	0.304615i
$501$		0			0
$502$	−19.8263	+	6.44196i	−0.884892	+	0.287519i
$503$	−10.4111	+	32.0422i	−0.464210	+	1.42869i	0.395764	+	0.918352i	$0.370480\pi$
$503$	−10.4111	+	32.0422i	−0.464210	+	1.42869i	−0.859974	+	0.510339i	$0.829520\pi$
$504$		0			0
$505$			22.2145i			0.988530i
$506$	36.5557	−	6.48500i	1.62510	−	0.288293i
$507$		0			0
$508$	−24.8126	+	34.1517i	−1.10088	+	1.51524i
$509$	−20.9648	−	6.81188i	−0.929248	−	0.301931i	−0.194993	−	0.980805i	$-0.562468\pi$
$509$	−20.9648	−	6.81188i	−0.929248	−	0.301931i	−0.734255	+	0.678874i	$0.762468\pi$
$510$		0			0
$511$	−1.92104	+	1.39572i	−0.0849819	+	0.0617429i
$512$	−22.3257	+	16.2206i	−0.986666	+	0.716855i
$513$		0			0
$514$	30.0531	+	9.76484i	1.32558	+	0.430709i
$515$	26.2367	−	36.1117i	1.15613	−	1.59127i
$516$		0			0
$517$	−8.25418	−	15.4849i	−0.363018	−	0.681027i
$518$		−	29.1588i		−	1.28116i
$519$		0			0
$520$	2.52685	−	7.77684i	0.110810	−	0.341037i
$521$	23.0301	−	7.48292i	1.00896	−	0.327833i	0.242523	−	0.970146i	$-0.422025\pi$
$521$	23.0301	−	7.48292i	1.00896	−	0.327833i	0.766442	+	0.642313i	$0.222025\pi$
$522$		0			0
$523$	−0.785047	−	1.08052i	−0.0343277	−	0.0472480i	0.791508	−	0.611159i	$-0.209296\pi$
$523$	−0.785047	−	1.08052i	−0.0343277	−	0.0472480i	−0.825836	+	0.563911i	$0.809296\pi$
$524$	−11.0876	−	34.1241i	−0.484363	−	1.49072i
$525$		0			0
$526$	−10.1723	−	7.39062i	−0.443534	−	0.322247i
$527$	7.93917			0.345836
$528$		0			0
$529$	−4.81321			−0.209270
$530$	21.1791	+	15.3875i	0.919961	+	0.668391i
$531$		0			0
$532$	−9.53667	−	29.3508i	−0.413467	−	1.27252i
$533$	2.00325	+	2.75724i	0.0867705	+	0.119429i
$534$		0			0
$535$	48.5175	−	15.7643i	2.09759	−	0.681549i
$536$	−2.19155	+	6.74489i	−0.0946604	+	0.291335i
$537$		0			0
$538$			14.3392i			0.618207i
$539$	10.5458	+	1.47092i	0.454239	+	0.0633570i
$540$		0			0
$541$	22.6301	−	31.1477i	0.972944	−	1.33914i	0.0323981	−	0.999475i	$-0.489686\pi$
$541$	22.6301	−	31.1477i	0.972944	−	1.33914i	0.940546	−	0.339667i	$-0.110314\pi$
$542$	12.7836	+	4.15363i	0.549101	+	0.178414i
$543$		0			0
$544$	−6.41743	+	4.66253i	−0.275145	+	0.199904i
$545$	1.08417	−	0.787693i	0.0464406	−	0.0337411i
$546$		0			0
$547$	−29.9931	−	9.74534i	−1.28241	−	0.416681i	−0.412983	−	0.910739i	$-0.635513\pi$
$547$	−29.9931	−	9.74534i	−1.28241	−	0.416681i	−0.869429	+	0.494058i	$0.835513\pi$
$548$	3.54690	−	4.88189i	0.151516	−	0.208544i
$549$		0			0
$550$	26.9947	+	3.76521i	1.15106	+	0.160549i
$551$			23.0984i			0.984025i
$552$		0			0
$553$	11.5676	−	35.6015i	0.491905	−	1.51393i
$554$	4.19989	−	1.36463i	0.178436	−	0.0579775i
$555$		0			0
$556$	6.28021	+	8.64396i	0.266340	+	0.366586i
$557$	−4.42923	−	13.6318i	−0.187673	−	0.577597i	0.812312	−	0.583224i	$-0.198209\pi$
$557$	−4.42923	−	13.6318i	−0.187673	−	0.577597i	−0.999984	+	0.00562684i	$0.998209\pi$
$558$		0			0
$559$	6.82566	+	4.95913i	0.288695	+	0.209749i
$560$	26.0218			1.09962
$561$		0			0
$562$	15.2743			0.644307
$563$	−11.7638	−	8.54689i	−0.495785	−	0.360209i	0.311620	−	0.950207i	$-0.399128\pi$
$563$	−11.7638	−	8.54689i	−0.495785	−	0.360209i	−0.807405	+	0.589998i	$0.799128\pi$
$564$		0			0
$565$	3.83254	+	11.7953i	0.161236	+	0.496234i
$566$	30.0398	+	41.3463i	1.26267	+	1.73791i
$567$		0			0
$568$	−9.79110	+	3.18132i	−0.410826	+	0.133485i
$569$	−4.80561	+	14.7902i	−0.201462	+	0.620035i	0.798378	+	0.602156i	$0.205691\pi$
$569$	−4.80561	+	14.7902i	−0.201462	+	0.620035i	−0.999840	+	0.0178794i	$0.994309\pi$
$570$		0			0
$571$		−	30.8824i		−	1.29239i	−0.763172	−	0.646195i	$-0.776359\pi$
$571$		−	30.8824i		−	1.29239i	0.763172	−	0.646195i	$-0.223641\pi$
$572$	10.0045	+	18.7686i	0.418311	+	0.784757i
$573$		0			0
$574$	5.30808	−	7.30594i	0.221555	−	0.304944i
$575$	−19.4194	−	6.30976i	−0.809846	−	0.263135i
$576$		0			0
$577$	−32.9843	+	23.9645i	−1.37316	+	0.997656i	−0.375672	+	0.926753i	$0.622588\pi$
$577$	−32.9843	+	23.9645i	−1.37316	+	0.997656i	−0.997483	+	0.0709027i	$0.977412\pi$
$578$	27.4820	−	19.9668i	1.14310	−	0.830511i
$579$		0			0
$580$	42.5226	+	13.8164i	1.76565	+	0.573696i
$581$	5.07429	−	6.98416i	0.210517	−	0.289752i
$582$		0			0
$583$	−13.5223	+	2.39887i	−0.560038	+	0.0993510i
$584$			0.797015i			0.0329807i
$585$		0			0
$586$	−14.2833	+	43.9595i	−0.590039	+	1.81595i
$587$	−17.1307	+	5.56610i	−0.707059	+	0.229737i	−0.640403	−	0.768039i	$-0.721233\pi$
$587$	−17.1307	+	5.56610i	−0.707059	+	0.229737i	−0.0666554	+	0.997776i	$0.521233\pi$
$588$		0			0
$589$	−18.0260	−	24.8106i	−0.742747	−	1.02230i
$590$	−22.7123	−	69.9013i	−0.935050	−	2.87779i
$591$		0			0
$592$	9.50941	+	6.90899i	0.390834	+	0.283958i
$593$	−12.6974			−0.521422			−0.260711	−	0.965417i	$-0.583957\pi$
$593$	−12.6974			−0.521422			−0.260711	+	0.965417i	$0.583957\pi$
$594$		0			0
$595$	9.49848			0.389400
$596$	8.05025	+	5.84885i	0.329751	+	0.239578i
$597$		0			0
$598$	−8.85427	−	27.2506i	−0.362078	−	1.11436i
$599$	−5.69678	−	7.84094i	−0.232764	−	0.320372i	0.676618	−	0.736334i	$-0.263445\pi$
$599$	−5.69678	−	7.84094i	−0.232764	−	0.320372i	−0.909382	+	0.415962i	$0.863445\pi$
$600$		0			0
$601$	−4.82038	+	1.56624i	−0.196627	+	0.0638881i	−0.405675	−	0.914017i	$-0.632964\pi$
$601$	−4.82038	+	1.56624i	−0.196627	+	0.0638881i	0.209048	+	0.977905i	$0.432964\pi$
$602$	6.90830	−	21.2616i	0.281561	−	0.866556i
$603$		0			0
$604$			43.3147i			1.76245i
$605$	−25.7763	+	20.2252i	−1.04796	+	0.822273i
$606$		0			0
$607$	16.9860	−	23.3793i	0.689442	−	0.948935i	−0.310557	−	0.950555i	$-0.600516\pi$
$607$	16.9860	−	23.3793i	0.689442	−	0.948935i	0.999999	+	0.00161969i	$0.000515563\pi$
$608$	29.1417	+	9.46870i	1.18185	+	0.384006i
$609$		0			0
$610$	41.0641	−	29.8348i	1.66264	−	1.20798i
$611$	−10.9562	+	7.96014i	−0.443240	+	0.322033i
$612$		0			0
$613$	−29.6117	−	9.62142i	−1.19600	−	0.388606i	−0.357715	−	0.933831i	$-0.616444\pi$
$613$	−29.6117	−	9.62142i	−1.19600	−	0.388606i	−0.838290	+	0.545225i	$0.816444\pi$
$614$	−34.6093	+	47.6356i	−1.39672	+	1.92241i
$615$		0			0
$616$	7.88736	−	8.18463i	0.317791	−	0.329768i
$617$		−	28.7025i		−	1.15552i	−0.816207	−	0.577760i	$-0.803927\pi$
$617$		−	28.7025i		−	1.15552i	0.816207	−	0.577760i	$-0.196073\pi$
$618$		0			0
$619$	4.88396	−	15.0313i	0.196303	−	0.604158i	−0.803656	−	0.595094i	$-0.797115\pi$
$619$	4.88396	−	15.0313i	0.196303	−	0.604158i	0.999959	−	0.00906388i	$-0.00288516\pi$
$620$	−56.4570	+	18.3440i	−2.26737	+	0.736712i
$621$		0			0
$622$	−27.1329	−	37.3453i	−1.08793	−	1.49741i
$623$	9.03767	+	27.8151i	0.362086	+	1.11439i
$624$		0			0
$625$	23.7595	+	17.2623i	0.950380	+	0.690492i
$626$	11.8329			0.472937
$627$		0			0
$628$	0.913056			0.0364349
$629$	3.47113	+	2.52192i	0.138403	+	0.100556i
$630$		0			0
$631$	9.43085	+	29.0252i	0.375436	+	1.15547i	0.943184	+	0.332271i	$0.107815\pi$
$631$	9.43085	+	29.0252i	0.375436	+	1.15547i	−0.567748	+	0.823203i	$0.692185\pi$
$632$	−7.38530	−	10.1650i	−0.293771	−	0.404342i
$633$		0			0
$634$	−27.5537	+	8.95275i	−1.09430	+	0.355559i
$635$	−15.5089	+	47.7315i	−0.615452	+	1.89417i
$636$		0			0
$637$		−	8.21767i		−	0.325596i
$638$	−37.2222	+	19.8411i	−1.47364	+	0.785518i
$639$		0			0
$640$	14.5424	−	20.0159i	0.574839	−	0.791197i
$641$	−17.2873	−	5.61698i	−0.682807	−	0.221858i	−0.0529832	−	0.998595i	$-0.516873\pi$
$641$	−17.2873	−	5.61698i	−0.682807	−	0.221858i	−0.629824	+	0.776738i	$0.716873\pi$
$642$		0			0
$643$	−7.37203	+	5.35609i	−0.290725	+	0.211224i	−0.723582	−	0.690239i	$-0.757505\pi$
$643$	−7.37203	+	5.35609i	−0.290725	+	0.211224i	0.432857	+	0.901463i	$0.357505\pi$
$644$	−34.1559	+	24.8157i	−1.34593	+	0.977875i
$645$		0			0
$646$	7.76655	+	2.52350i	0.305571	+	0.0992859i
$647$	−18.9534	+	26.0871i	−0.745136	+	1.02559i	0.253171	+	0.967422i	$0.418527\pi$
$647$	−18.9534	+	26.0871i	−0.745136	+	1.02559i	−0.998307	+	0.0581699i	$0.981473\pi$
$648$		0			0
$649$	34.6728	+	16.8664i	1.36103	+	0.662065i
$650$		−	21.0353i		−	0.825073i
$651$		0			0
$652$	2.33981	−	7.20120i	0.0916340	−	0.282021i
$653$	−20.4313	+	6.63853i	−0.799538	+	0.259786i	−0.680160	−	0.733063i	$-0.738090\pi$
$653$	−20.4313	+	6.63853i	−0.799538	+	0.259786i	−0.119378	+	0.992849i	$0.538090\pi$
$654$		0			0
$655$	−25.0737	−	34.5109i	−0.979709	−	1.34845i
$656$	1.12493	+	3.46219i	0.0439213	+	0.135176i
$657$		0			0
$658$	29.0309	+	21.0922i	1.13174	+	0.822260i
$659$	−30.1358			−1.17393			−0.586963	−	0.809614i	$-0.699676\pi$
$659$	−30.1358			−1.17393			−0.586963	+	0.809614i	$0.699676\pi$
$660$		0			0
$661$	−44.9664			−1.74899			−0.874496	−	0.485033i	$-0.838808\pi$
$661$	−44.9664			−1.74899			−0.874496	+	0.485033i	$0.838808\pi$
$662$	−13.6610	−	9.92532i	−0.530951	−	0.385758i
$663$		0			0
$664$	−0.895419	−	2.75582i	−0.0347490	−	0.106946i
$665$	−21.5664	−	29.6836i	−0.836309	−	1.15108i
$666$		0			0
$667$	30.0526	−	9.76467i	1.16364	−	0.378090i
$668$	−5.96050	+	18.3445i	−0.230619	+	0.709771i
$669$		0			0
$670$			41.8046i			1.61505i
$671$	−3.67842	+	26.3725i	−0.142004	+	1.01810i
$672$		0			0
$673$	−23.7932	+	32.7486i	−0.917162	+	1.26236i	0.0474995	+	0.998871i	$0.484875\pi$
$673$	−23.7932	+	32.7486i	−0.917162	+	1.26236i	−0.964661	+	0.263494i	$0.915125\pi$
$674$	63.3275	+	20.5764i	2.43929	+	0.792572i
$675$		0			0
$676$	−13.0692	+	9.49536i	−0.502663	+	0.365206i
$677$	26.3382	−	19.1358i	1.01226	−	0.735448i	0.0475763	−	0.998868i	$-0.484850\pi$
$677$	26.3382	−	19.1358i	1.01226	−	0.735448i	0.964681	+	0.263419i	$0.0848503\pi$
$678$		0			0
$679$	−28.3590	−	9.21441i	−1.08832	−	0.353617i
$680$	1.87396	−	2.57928i	0.0718631	−	0.0989111i
$681$		0			0
$682$	24.4974	−	50.3601i	0.938054	−	1.92839i
$683$			9.42972i			0.360818i	0.983592	+	0.180409i	$0.0577422\pi$
$683$			9.42972i			0.360818i	−0.983592	+	0.180409i	$0.942258\pi$
$684$		0			0
$685$	2.21696	−	6.82309i	0.0847055	−	0.260697i
$686$	24.4443	−	7.94244i	0.933289	−	0.303244i
$687$		0			0
$688$	5.29704	+	7.29076i	0.201948	+	0.277957i
$689$	3.27528	+	10.0803i	0.124778	+	0.384028i
$690$		0			0
$691$	−6.24048	−	4.53397i	−0.237399	−	0.172480i	0.462725	−	0.886502i	$-0.346872\pi$
$691$	−6.24048	−	4.53397i	−0.237399	−	0.172480i	−0.700124	+	0.714022i	$0.746872\pi$
$692$	−27.8239			−1.05771
$693$		0			0
$694$	−4.82158			−0.183025
$695$	10.2768	+	7.46652i	0.389821	+	0.283221i
$696$		0			0
$697$	0.410624	+	1.26377i	0.0155535	+	0.0478687i
$698$	34.1155	+	46.9560i	1.29129	+	1.77731i
$699$		0			0
$700$	−29.4777	+	9.57787i	−1.11415	+	0.362010i
$701$	4.21571	−	12.9746i	0.159225	−	0.490044i	−0.839339	−	0.543608i	$-0.817058\pi$
$701$	4.21571	−	12.9746i	0.159225	−	0.490044i	0.998564	+	0.0535633i	$0.0170579\pi$
$702$		0			0
$703$		−	16.5736i		−	0.625086i
$704$	6.60589	+	37.2371i	0.248969	+	1.40343i
$705$		0			0
$706$	−24.9189	+	34.2980i	−0.937837	+	1.29082i
$707$	22.6652	+	7.36438i	0.852414	+	0.276966i
$708$		0			0
$709$	−13.1477	+	9.55236i	−0.493772	+	0.358746i	−0.806633	−	0.591052i	$-0.798713\pi$
$709$	−13.1477	+	9.55236i	−0.493772	+	0.358746i	0.312861	+	0.949799i	$0.398713\pi$
$710$	−49.0952	+	35.6697i	−1.84251	+	1.33866i
$711$		0			0
$712$	9.33615	+	3.03350i	0.349887	+	0.113685i
$713$	−24.6599	+	33.9415i	−0.923522	+	1.27112i
$714$		0			0
$715$	18.2076	+	17.5463i	0.680927	+	0.656195i
$716$		−	20.7516i		−	0.775523i
$717$		0			0
$718$	−14.0270	+	43.1706i	−0.523482	+	1.61111i
$719$	−12.0892	+	3.92803i	−0.450852	+	0.146491i	−0.525637	−	0.850709i	$-0.676173\pi$
$719$	−12.0892	+	3.92803i	−0.450852	+	0.146491i	0.0747848	+	0.997200i	$0.476173\pi$
$720$		0			0
$721$	−28.1467	−	38.7407i	−1.04824	−	1.44278i
$722$	2.71444	+	8.35420i	0.101021	+	0.310911i
$723$		0			0
$724$	−34.6806	−	25.1970i	−1.28890	−	0.936437i
$725$	23.1982			0.861560
$726$		0			0
$727$	29.4959			1.09394			0.546972	−	0.837151i	$-0.315781\pi$
$727$	29.4959			1.09394			0.546972	+	0.837151i	$0.315781\pi$
$728$	−7.09697	−	5.15625i	−0.263031	−	0.191103i
$729$		0			0
$730$	1.45179	+	4.46816i	0.0537333	+	0.165374i
$731$	1.93353	+	2.66127i	0.0715141	+	0.0984308i
$732$		0			0
$733$	36.6838	−	11.9193i	1.35495	−	0.440249i	0.460594	−	0.887611i	$-0.347637\pi$
$733$	36.6838	−	11.9193i	1.35495	−	0.440249i	0.894353	+	0.447362i	$0.147637\pi$
$734$	−12.6276	+	38.8636i	−0.466092	+	1.43448i
$735$		0			0
$736$		−	41.9181i		−	1.54512i
$737$	−15.7916	−	15.2180i	−0.581689	−	0.560562i
$738$		0			0
$739$	−13.6543	+	18.7936i	−0.502282	+	0.691332i	−0.982594	−	0.185766i	$-0.940523\pi$
$739$	−13.6543	+	18.7936i	−0.502282	+	0.691332i	0.480312	+	0.877098i	$0.340523\pi$
$740$	−30.5109	−	9.91360i	−1.12160	−	0.364431i
$741$		0			0
$742$	22.7209	−	16.5077i	0.834111	−	0.606017i
$743$	−2.99034	+	2.17261i	−0.109705	+	0.0797052i	−0.641285	−	0.767303i	$-0.721598\pi$
$743$	−2.99034	+	2.17261i	−0.109705	+	0.0797052i	0.531580	+	0.847008i	$0.321598\pi$
$744$		0			0
$745$	11.2513	+	3.65577i	0.412215	+	0.133937i
$746$	−8.60366	+	11.8419i	−0.315002	+	0.433564i
$747$		0			0
$748$	1.44847	+	8.16498i	0.0529613	+	0.298541i
$749$		−	54.7281i		−	1.99972i
$750$		0			0
$751$	−15.2699	+	46.9958i	−0.557206	+	1.71490i	0.132841	+	0.991137i	$0.457590\pi$
$751$	−15.2699	+	46.9958i	−0.557206	+	1.71490i	−0.690046	+	0.723765i	$0.742410\pi$
$752$	−13.7574	+	4.47005i	−0.501680	+	0.163006i
$753$		0			0
$754$	19.1343	+	26.3361i	0.696831	+	0.959106i
$755$	15.9134	+	48.9763i	0.579147	+	1.78243i
$756$		0			0
$757$	−34.6804	−	25.1968i	−1.26048	−	0.915792i	−0.261698	−	0.965150i	$-0.584282\pi$
$757$	−34.6804	−	25.1968i	−1.26048	−	0.915792i	−0.998781	+	0.0493580i	$0.984282\pi$
$758$	−72.8820			−2.64719
$759$		0			0
$760$	−12.3153			−0.446724
$761$	33.9827	+	24.6899i	1.23187	+	0.895008i	0.997029	−	0.0770250i	$-0.0245421\pi$
$761$	33.9827	+	24.6899i	1.23187	+	0.895008i	0.234844	+	0.972033i	$0.424542\pi$
$762$		0			0
$763$	−0.444262	−	1.36730i	−0.0160834	−	0.0494995i
$764$	−16.0442	−	22.0829i	−0.580457	−	0.798931i
$765$		0			0
$766$	3.22889	−	1.04913i	0.116665	−	0.0379066i
$767$	9.19556	−	28.3010i	0.332032	−	1.02189i
$768$		0			0
$769$			4.13165i			0.148991i	0.997221	+	0.0744955i	$0.0237346\pi$
$769$			4.13165i			0.148991i	−0.997221	+	0.0744955i	$0.976265\pi$
$770$	29.3088	−	60.2511i	1.05622	−	2.17130i
$771$		0			0
$772$	−15.9407	+	21.9405i	−0.573717	+	0.789654i
$773$	21.2989	+	6.92044i	0.766069	+	0.248911i	0.665882	−	0.746057i	$-0.268056\pi$
$773$	21.2989	+	6.92044i	0.766069	+	0.248911i	0.100188	+	0.994969i	$0.468056\pi$
$774$		0			0
$775$	−24.9178	+	18.1039i	−0.895075	+	0.650310i
$776$	−8.09712	+	5.88290i	−0.290670	+	0.211184i
$777$		0			0
$778$	−47.9232	−	15.5712i	−1.71813	−	0.558254i
$779$	3.01707	−	4.15264i	0.108098	−	0.148784i
$780$		0			0
$781$	4.39783	−	31.5303i	0.157367	−	1.12824i
$782$		−	11.1716i		−	0.399495i
$783$		0			0
$784$	2.71243	−	8.34801i	0.0968726	−	0.298143i
$785$	1.03240	−	0.335447i	0.0368480	−	0.0119726i
$786$		0			0
$787$	−4.93902	−	6.79798i	−0.176057	−	0.242322i	0.711864	−	0.702317i	$-0.247851\pi$
$787$	−4.93902	−	6.79798i	−0.176057	−	0.242322i	−0.887921	+	0.459995i	$0.847851\pi$
$788$	−1.38423	−	4.26023i	−0.0493112	−	0.151764i
$789$		0			0
$790$	−59.9187	−	43.5335i	−2.13181	−	1.54885i
$791$	13.3052			0.473080
$792$		0			0
$793$	20.5504			0.729768
$794$	25.9623	+	18.8627i	0.921369	+	0.669413i
$795$		0			0
$796$	0.413648	+	1.27308i	0.0146614	+	0.0451231i
$797$	4.60369	+	6.33643i	0.163071	+	0.224448i	0.882731	−	0.469879i	$-0.155702\pi$
$797$	4.60369	+	6.33643i	0.163071	+	0.224448i	−0.719660	+	0.694327i	$0.755702\pi$
$798$		0			0
$799$	−5.02172	+	1.63166i	−0.177656	+	0.0577239i
$800$	9.50961	−	29.2676i	0.336216	−	1.03476i
$801$		0			0
$802$		−	55.2798i		−	1.95200i
$803$	−2.21632	−	1.07812i	−0.0782124	−	0.0380460i
$804$		0			0
$805$	−29.5033	+	40.6078i	−1.03986	+	1.43124i
$806$	−41.1054	−	13.3560i	−1.44788	−	0.470443i
$807$		0			0
$808$	6.47141	−	4.70176i	0.227664	−	0.165407i
$809$	32.0318	−	23.2725i	1.12618	−	0.818216i	0.141044	−	0.990003i	$-0.454954\pi$
$809$	32.0318	−	23.2725i	1.12618	−	0.818216i	0.985134	+	0.171787i	$0.0549541\pi$
$810$		0			0
$811$	−43.7729	−	14.2227i	−1.53708	−	0.499426i	−0.586508	−	0.809944i	$-0.699498\pi$
$811$	−43.7729	−	14.2227i	−1.53708	−	0.499426i	−0.950568	+	0.310518i	$0.899498\pi$
$812$	28.1936	−	38.8052i	0.989401	−	1.36179i
$813$		0			0
$814$	26.7078	−	14.2365i	0.936107	−	0.498987i
$815$		−	9.00208i		−	0.315329i
$816$		0			0
$817$	3.92662	−	12.0849i	0.137375	−	0.422797i
$818$	17.3228	−	5.62853i	0.605679	−	0.196797i
$819$		0			0
$820$	−5.84005	−	8.03814i	−0.203943	−	0.280704i
$821$	5.42862	+	16.7076i	0.189460	+	0.583099i	0.999997	−	0.00258952i	$-0.000824271\pi$
$821$	5.42862	+	16.7076i	0.189460	+	0.583099i	−0.810536	+	0.585688i	$0.800824\pi$
$822$		0			0
$823$	−35.6517	−	25.9025i	−1.24274	−	0.902904i	−0.244963	−	0.969532i	$-0.578776\pi$
$823$	−35.6517	−	25.9025i	−1.24274	−	0.902904i	−0.997778	+	0.0666279i	$0.978776\pi$
$824$	−16.0730			−0.559929
$825$		0			0
$826$	−78.8492			−2.74351
$827$	41.6792	+	30.2817i	1.44933	+	1.05300i	0.985988	+	0.166818i	$0.0533493\pi$
$827$	41.6792	+	30.2817i	1.44933	+	1.05300i	0.463341	+	0.886180i	$0.346651\pi$
$828$		0			0
$829$	6.34753	+	19.5357i	0.220459	+	0.678503i	0.998721	+	0.0505630i	$0.0161016\pi$
$829$	6.34753	+	19.5357i	0.220459	+	0.678503i	−0.778262	+	0.627940i	$0.783898\pi$
$830$	−10.0397	−	13.8184i	−0.348481	−	0.479643i
$831$		0			0
$832$	27.7586	−	9.01932i	0.962356	−	0.312689i
$833$	0.990093	−	3.04719i	0.0343047	−	0.105579i
$834$		0			0
$835$			22.9322i			0.793600i
$836$	22.2275	−	23.0653i	0.768754	−	0.797729i
$837$		0			0
$838$	−22.3175	+	30.7174i	−0.770945	+	1.06111i
$839$	40.8430	+	13.2707i	1.41006	+	0.458155i	0.912429	−	0.409235i	$-0.134204\pi$
$839$	40.8430	+	13.2707i	1.41006	+	0.458155i	0.497628	+	0.867391i	$0.334204\pi$
$840$		0			0
$841$	−5.58256	+	4.05597i	−0.192502	+	0.139861i
$842$	5.97597	−	4.34180i	0.205946	−	0.149628i
$843$		0			0
$844$	−12.2639	−	3.98478i	−0.422140	−	0.137162i
$845$	−11.2890	+	15.5380i	−0.388354	+	0.534523i
$846$		0			0
$847$	12.0905	+	33.0043i	0.415433	+	1.13404i
$848$			11.3213i			0.388773i
$849$		0			0
$850$	2.53441	−	7.80010i	0.0869294	−	0.267541i
$851$	−21.5634	+	7.00637i	−0.739184	+	0.240175i
$852$		0			0
$853$	15.2572	+	20.9997i	0.522396	+	0.719016i	0.985948	−	0.167053i	$-0.0534252\pi$
$853$	15.2572	+	20.9997i	0.522396	+	0.719016i	−0.463552	+	0.886070i	$0.653425\pi$
$854$	−16.8269	−	51.7880i	−0.575806	−	1.77215i
$855$		0			0
$856$	−14.8613	−	10.7973i	−0.507947	−	0.369045i
$857$	−10.4772			−0.357895			−0.178948	−	0.983859i	$-0.557269\pi$
$857$	−10.4772			−0.357895			−0.178948	+	0.983859i	$0.557269\pi$
$858$		0			0
$859$	23.6244			0.806053			0.403026	−	0.915188i	$-0.367958\pi$
$859$	23.6244			0.806053			0.403026	+	0.915188i	$0.367958\pi$
$860$	−19.8987	−	14.4573i	−0.678541	−	0.492989i
$861$		0			0
$862$	18.5566	+	57.1115i	0.632042	+	1.94522i
$863$	−2.46666	−	3.39507i	−0.0839661	−	0.115569i	0.764968	−	0.644069i	$-0.222755\pi$
$863$	−2.46666	−	3.39507i	−0.0839661	−	0.115569i	−0.848934	+	0.528499i	$0.822755\pi$
$864$		0			0
$865$	−31.4607	+	10.2222i	−1.06970	+	0.347566i
$866$	2.18965	−	6.73906i	0.0744075	−	0.229003i
$867$		0			0
$868$			63.6839i			2.16157i
$869$	38.2567	−	6.78675i	1.29777	−	0.230225i
$870$		0			0
$871$	−9.94855	+	13.6930i	−0.337094	+	0.463970i
$872$	−0.458934	−	0.149117i	−0.0155415	−	0.00504973i
$873$		0			0
$874$	−34.9122	+	25.3652i	−1.18092	+	0.857991i
$875$	8.68757	−	6.31189i	0.293694	−	0.213381i
$876$		0			0
$877$	−30.5461	−	9.92504i	−1.03147	−	0.335145i	−0.256099	−	0.966651i	$-0.582437\pi$
$877$	−30.5461	−	9.92504i	−1.03147	−	0.335145i	−0.775371	+	0.631506i	$0.782437\pi$
$878$	−18.9141	+	26.0330i	−0.638319	+	0.878570i
$879$		0			0
$880$	12.7048	+	23.8345i	0.428280	+	0.803459i
$881$		−	16.9977i		−	0.572666i	−0.958130	−	0.286333i	$-0.907564\pi$
$881$		−	16.9977i		−	0.572666i	0.958130	−	0.286333i	$-0.0924364\pi$
$882$		0			0
$883$	6.18492	−	19.0352i	0.208139	−	0.640586i	−0.791431	−	0.611259i	$-0.790663\pi$
$883$	6.18492	−	19.0352i	0.208139	−	0.640586i	0.999570	−	0.0293274i	$-0.00933653\pi$
$884$	6.08662	−	1.97766i	0.204715	−	0.0665160i
$885$		0			0
$886$	13.1696	+	18.1264i	0.442441	+	0.608968i
$887$	0.00102104	+	0.00314245i	3.42833e−5	+	0.000105513i	0.951074	−	0.308964i	$-0.0999823\pi$
$887$	0.00102104	+	0.00314245i	3.42833e−5	+	0.000105513i	−0.951039	+	0.309070i	$0.899982\pi$
$888$		0			0
$889$	43.5587	+	31.6473i	1.46091	+	1.06141i
$890$	57.8652			1.93965
$891$		0			0
$892$	10.5206			0.352256
$893$	16.5009	+	11.9886i	0.552183	+	0.401185i
$894$		0			0
$895$	−7.62392	−	23.4640i	−0.254839	−	0.784315i
$896$	−15.6011	−	21.4730i	−0.521195	−	0.717363i
$897$		0			0
$898$	31.7508	−	10.3165i	1.05954	−	0.344265i
$899$	14.7292	−	45.3319i	0.491247	−	1.51190i
$900$		0			0
$901$			4.13249i			0.137673i
$902$	9.28343	+	1.29485i	0.309104	+	0.0431137i
$903$		0			0
$904$	2.62500	−	3.61300i	0.0873061	−	0.120167i
$905$	−48.4708	−	15.7491i	−1.61122	−	0.523518i
$906$		0			0
$907$	24.6575	−	17.9148i	0.818740	−	0.594850i	−0.0976112	−	0.995225i	$-0.531120\pi$
$907$	24.6575	−	17.9148i	0.818740	−	0.594850i	0.916351	+	0.400375i	$0.131120\pi$
$908$	33.8843	−	24.6184i	1.12449	−	0.816990i
$909$		0			0
$910$	−49.1788	−	15.9791i	−1.63026	−	0.529703i
$911$	22.3820	−	30.8062i	0.741549	−	1.02065i	−0.256979	−	0.966417i	$-0.582727\pi$
$911$	22.3820	−	30.8062i	0.741549	−	1.02065i	0.998528	−	0.0542375i	$-0.0172728\pi$
$912$		0			0
$913$	8.87455	+	1.23782i	0.293705	+	0.0409658i
$914$			6.47759i			0.214260i
$915$		0			0
$916$	−20.1268	+	61.9439i	−0.665008	+	2.04668i
$917$	−43.5235	+	14.1416i	−1.43727	+	0.466998i
$918$		0			0
$919$	14.7418	+	20.2904i	0.486288	+	0.669318i	0.979698	−	0.200479i	$-0.0642497\pi$
$919$	14.7418	+	20.2904i	0.486288	+	0.669318i	−0.493410	+	0.869797i	$0.664250\pi$
$920$	5.20621	+	16.0231i	0.171644	+	0.528265i
$921$		0			0
$922$	0.844325	+	0.613438i	0.0278064	+	0.0202025i
$923$	−24.5696			−0.808718
$924$		0			0
$925$	−16.6452			−0.547292
$926$	−15.4265	−	11.2080i	−0.506948	−	0.368319i
$927$		0			0
$928$	14.7166	+	45.2931i	0.483096	+	1.48682i
$929$	3.82694	+	5.26733i	0.125558	+	0.172815i	0.867168	−	0.498015i	$-0.165938\pi$
$929$	3.82694	+	5.26733i	0.125558	+	0.172815i	−0.741610	+	0.670831i	$0.765938\pi$
$930$		0			0
$931$	−11.7708	+	3.82455i	−0.385771	+	0.125345i
$932$	13.4727	−	41.4648i	0.441314	−	1.35822i
$933$		0			0
$934$			4.82063i			0.157736i
$935$	4.63753	+	8.70006i	0.151663	+	0.284522i
$936$		0			0
$937$	4.31370	−	5.93730i	0.140923	−	0.193963i	−0.732722	−	0.680528i	$-0.761750\pi$
$937$	4.31370	−	5.93730i	0.140923	−	0.193963i	0.873644	+	0.486565i	$0.161750\pi$
$938$	42.6529	+	13.8588i	1.39267	+	0.452505i
$939$		0			0
$940$	31.9404	−	23.2061i	1.04178	−	0.756898i
$941$	19.7910	−	14.3790i	0.645167	−	0.468741i	−0.216454	−	0.976293i	$-0.569449\pi$
$941$	19.7910	−	14.3790i	0.645167	−	0.468741i	0.861621	+	0.507551i	$0.169449\pi$
$942$		0			0
$943$	−6.67830	−	2.16991i	−0.217476	−	0.0706621i
$944$	18.6828	−	25.7147i	0.608073	−	0.836941i
$945$		0			0
$946$	22.8473	−	4.05311i	0.742828	−	0.131778i
$947$		−	36.2379i		−	1.17757i	−0.808288	−	0.588787i	$-0.799606\pi$
$947$		−	36.2379i		−	1.17757i	0.808288	−	0.588787i	$-0.200394\pi$
$948$		0			0
$949$	−0.587789	+	1.80903i	−0.0190805	+	0.0587236i
$950$	−30.1304	+	9.78996i	−0.977560	+	0.317628i
$951$		0			0
$952$	−2.01038	−	2.76705i	−0.0651569	−	0.0896807i
$953$	16.2642	+	50.0560i	0.526848	+	1.62147i	0.760632	+	0.649183i	$0.224889\pi$
$953$	16.2642	+	50.0560i	0.526848	+	1.62147i	−0.233784	+	0.972289i	$0.575111\pi$
$954$		0			0
$955$	−26.2543	−	19.0749i	−0.849570	−	0.617248i
$956$	−6.24310			−0.201916
$957$		0			0
$958$	24.5836			0.794259
$959$	−6.22660	−	4.52389i	−0.201067	−	0.146084i
$960$		0			0
$961$	9.97638	+	30.7041i	0.321819	+	0.990456i
$962$	−13.7293	−	18.8968i	−0.442651	−	0.609256i
$963$		0			0
$964$	54.4880	−	17.7042i	1.75494	−	0.570214i
$965$	−9.96357	+	30.6647i	−0.320739	+	0.987132i
$966$		0			0
$967$		−	21.1895i		−	0.681409i	−0.940171	−	0.340704i	$-0.889335\pi$
$967$		−	21.1895i		−	0.681409i	0.940171	−	0.340704i	$-0.110665\pi$
$968$	11.3476	+	3.22831i	0.364724	+	0.103762i
$969$		0			0
$970$	−34.6775	+	47.7294i	−1.11343	+	1.53250i
$971$	38.9482	+	12.6550i	1.24991	+	0.406119i	0.857887	−	0.513838i	$-0.171777\pi$
$971$	38.9482	+	12.6550i	1.24991	+	0.406119i	0.392019	+	0.919957i	$0.371777\pi$
$972$		0			0
$973$	11.0249	−	8.01008i	0.353443	−	0.256791i
$974$	−63.2741	+	45.9713i	−2.02743	+	1.47302i
$975$		0			0
$976$	20.8764	+	6.78315i	0.668237	+	0.217123i
$977$	35.9665	−	49.5036i	1.15067	−	1.58376i	0.409701	−	0.912220i	$-0.365633\pi$
$977$	35.9665	−	49.5036i	1.15067	−	1.58376i	0.740968	−	0.671540i	$-0.234367\pi$
$978$		0			0
$979$	−21.0645	+	21.8584i	−0.673223	+	0.698597i
$980$			23.9568i			0.765273i
$981$		0			0
$982$	9.13758	−	28.1226i	0.291592	−	0.897428i
$983$	54.8070	−	17.8079i	1.74807	−	0.567983i	0.752214	−	0.658919i	$-0.228986\pi$
$983$	54.8070	−	17.8079i	1.74807	−	0.567983i	0.995857	+	0.0909365i	$0.0289860\pi$
$984$		0			0
$985$	−3.13033	−	4.30853i	−0.0997405	−	0.137281i
$986$	3.92213	+	12.0711i	0.124906	+	0.384421i
$987$		0			0
$988$	−20.0001	−	14.5309i	−0.636288	−	0.462290i
$989$	−17.3832			−0.552754
$990$		0			0
$991$	−15.6063			−0.495750			−0.247875	−	0.968792i	$-0.579732\pi$
$991$	−15.6063			−0.495750			−0.247875	+	0.968792i	$0.579732\pi$
$992$	−51.1542	−	37.1657i	−1.62415	−	1.18001i
$993$		0			0
$994$	20.1179	+	61.9164i	0.638100	+	1.96387i
$995$	0.935432	+	1.28751i	0.0296552	+	0.0408169i
$996$		0			0
$997$	−10.8263	+	3.51767i	−0.342872	+	0.111406i	−0.475391	−	0.879775i	$-0.657693\pi$
$997$	−10.8263	+	3.51767i	−0.342872	+	0.111406i	0.132519	+	0.991180i	$0.457693\pi$
$998$	8.28469	−	25.4977i	0.262247	−	0.807115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.161.3		80
3.2	odd	2	inner	891.2.k.a.161.18		80
9.2	odd	6		99.2.p.a.95.9	yes	80
9.4	even	3		99.2.p.a.29.9	✓	80
9.5	odd	6		297.2.t.a.62.2		80
9.7	even	3		297.2.t.a.260.2		80
11.8	odd	10	inner	891.2.k.a.404.18		80
33.8	even	10	inner	891.2.k.a.404.3		80
99.41	even	30		297.2.t.a.8.2		80
99.52	odd	30		297.2.t.a.206.2		80
99.74	even	30		99.2.p.a.41.9	yes	80
99.85	odd	30		99.2.p.a.74.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.9	✓	80	9.4	even	3
99.2.p.a.41.9	yes	80	99.74	even	30
99.2.p.a.74.9	yes	80	99.85	odd	30
99.2.p.a.95.9	yes	80	9.2	odd	6
297.2.t.a.8.2		80	99.41	even	30
297.2.t.a.62.2		80	9.5	odd	6
297.2.t.a.206.2		80	99.52	odd	30
297.2.t.a.260.2		80	9.7	even	3
891.2.k.a.161.3		80	1.1	even	1	trivial
891.2.k.a.161.18		80	3.2	odd	2	inner
891.2.k.a.404.3		80	33.8	even	10	inner
891.2.k.a.404.18		80	11.8	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71719 - 1.24761i) q^{2} +(0.774180 + 2.38268i) q^{4} +(1.75074 + 2.40969i) q^{5} +(3.03899 - 0.987427i) q^{7} +(0.331430 - 1.02004i) q^{8} -6.32217i q^{10} +(2.38818 + 2.30144i) q^{11} +(1.50453 - 2.07081i) q^{13} +(-6.45046 - 2.09588i) q^{14} +(2.21191 - 1.60705i) q^{16} +(0.807393 - 0.586606i) q^{17} +(-3.66639 - 1.19128i) q^{19} +(-4.38614 + 6.03700i) q^{20} +(-1.22966 - 6.93154i) q^{22} +5.27382i q^{23} +(-1.19643 + 3.68223i) q^{25} +(-5.16715 + 1.67891i) q^{26} +(4.70544 + 6.47649i) q^{28} +(-1.85154 - 5.69844i) q^{29} +(6.43584 + 4.67591i) q^{31} -7.94833 q^{32} -2.11831 q^{34} +(7.69988 + 5.59429i) q^{35} +(1.32852 + 4.08876i) q^{37} +(4.80964 + 6.61990i) q^{38} +(3.03823 - 0.987180i) q^{40} +(-0.411450 + 1.26631i) q^{41} +3.29613i q^{43} +(-3.63471 + 7.47199i) q^{44} +(6.57970 - 9.05618i) q^{46} +(-5.03182 - 1.63494i) q^{47} +(2.59731 - 1.88706i) q^{49} +(6.64851 - 4.83042i) q^{50} +(6.09886 + 1.98164i) q^{52} +(-2.43390 + 3.34997i) q^{53} +(-1.36467 + 9.78400i) q^{55} -3.42715i q^{56} +(-3.93001 + 12.0953i) q^{58} +(11.0565 - 3.59249i) q^{59} +(4.71908 + 6.49525i) q^{61} +(-5.21785 - 16.0589i) q^{62} +(9.22499 + 6.70235i) q^{64} +7.62407 q^{65} -6.61239 q^{67} +(2.02276 + 1.46962i) q^{68} +(-6.24267 - 19.2130i) q^{70} +(-5.64201 - 7.76556i) q^{71} +(-0.706745 + 0.229635i) q^{73} +(2.81987 - 8.67867i) q^{74} -9.65810i q^{76} +(9.53014 + 4.63589i) q^{77} +(6.88586 - 9.47757i) q^{79} +(7.74499 + 2.51650i) q^{80} +(2.28641 - 1.66117i) q^{82} +(2.18571 - 1.58801i) q^{83} +(2.82708 + 0.918574i) q^{85} +(4.11230 - 5.66010i) q^{86} +(3.13907 - 1.67327i) q^{88} +9.15275i q^{89} +(2.52748 - 7.77878i) q^{91} +(-12.5658 + 4.08289i) q^{92} +(6.60084 + 9.08528i) q^{94} +(-3.54829 - 10.9205i) q^{95} +(-7.54954 - 5.48506i) q^{97} -6.81440 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Introduction

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